One day in 1956, in a happy accident of history, Elvis Presley, Jerry Lee Lewis, Carl Perkins and Johnny Cash hung out together at the Sun Records Studios in Memphis.

One day in 1956, in a happy accident of history, Elvis Presley, Jerry Lee Lewis, Carl Perkins and Johnny Cash hung out together at Sun Records Studios in Memphis. A famed photo shows the four, some rough recordings commemorated their jam session, and a journalist dubbed them the “million dollar quartet.” This new musical exploits that historical moment to create what might be called a fantasy revue. While it makes tentative stabs at building a story, “Million Dollar Quartet”mostly becomes a genuinely enjoyable concert that imagines the foursome creating music that’s more than the sum of their parts.

The show premiered in Florida, then had a successful run at Seattle’s Village Theater. Director Eric Schaeffer (“Glory Days”) has joined the creative team to co-direct with Floyd Mutrux for this Chicago stand, where the producers have rented the second space at the Goodman Theater, with a move to a midsized commercial house likely for a longer run.

The directors do a strong job of working with the multitalented performers to find the right balance of mimicry and honesty in the acting. Given the distinctness of these figures, it would be easy to let this go over the top, but here a lot of work has clearly been done to make it seem like they’re not working that hard. They also make sure to establish these men as being in their youth, before they became caricatures of themselves as fame and fortune distorted them.

Eddie Clendening captures the youthful Elvis, only a few months after he changed the world on “The Ed Sullivan Show.” Clendening doesn’t quite express the fullness of Elvis’ charisma, but a humble Elvis is exactly what this show calls for — a young musician, unpretentious among peers.

As Jerry Lee Lewis, who wasn’t yet a star but was invited to play on a Carl Perkins (Rob Lyons) recording, Levi Kreis makes the right nod to his character’s quirkiness without letting it dominate. In the most relaxed and convincing performance, Lance Guest plays Johnny Cash with a depiction of his signature bass-baritone that comes off with sincerity.

And, of course, that’s not even mentioning the musicianship of all of them, which is at a very high level.

Book writers Colin Escott and Mutrux take a stab at injecting some drama into the jam session, and they come up with good possible plotlines to work with, focusing on the man who brought them together, producer Sam Phillips (Brian McCaskill). They imagine this as the day Cash and Perkins tell Phillips they’re moving on to another label, a situation that properly captures Phillips as a man who would nurture grand talent only to see them move on.

There’s certainly more that could be done with the book — the scenes never attain either a naturalism that would create a structure for the structurelessness of the jam session or storylines to develop interest in the songs or, to be honest, the players. In other words, this is a show that’s all about the music, and “Million Dollar Quartet” is ultimately more a revue than a musical proper.

But as a revue, it satisfies. Song list becomes a fine tribute to early rock ‘n’ roll, and while there are standard classics (“Blue Suede Shoes,” “Great Balls of Fire”), it’s not purely a playlist of greatest hits. Most important, this group sounds great together.

Ultimately, the creators and performers do just enough to keep this show from feeling only like a legends concert, whose natural home would be a small-scale venue within a Las Vegas casino. While that may be its ultimate destination , “Million Dollar Quartet” also has a legit future driven by the popularity of its subjects and the sheer vitality of the musical performances.

They do rock the house.

Million Dollar Quartet

Goodman Theater in the Owen, Chicago; 387 seats; $49 top

Production

A Dee Gee Theatricals, John Cossette Prods. Productions and Northern Lights presentation of a musical in one act with book by Colin Escott and Floyd Mutrux. Directed by Mutrux, and Eric Schaeffer.